Find the x- and y-intercepts of f. f(x) = (x - 1)(x - 5)(x+1)^2
Question
Find the x- and y-intercepts of f. f(x) = (x - 1)(x - 5)(x+1)^2
Solution
To find the x-intercepts of the function f(x) = (x - 1)(x - 5)(x+1)^2, we set f(x) equal to zero and solve for x.
0 = (x - 1)(x - 5)(x+1)^2
This equation is equal to zero if any of the factors are equal to zero. So, we set each factor equal to zero and solve for x:
x - 1 = 0 => x = 1 x - 5 = 0 => x = 5 (x+1)^2 = 0 => x = -1
So, the x-intercepts of the function are x = 1, x = 5, and x = -1.
To find the y-intercept of the function, we set x equal to zero and solve for f(x):
f(0) = (0 - 1)(0 - 5)(0+1)^2 = 151 = 5
So, the y-intercept of the function is y = 5.
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